\(\mathcal {F}\)  is a space of functions, and \(J(\mu )\)  is a penalty function. Suppose \(\mathcal {F} = \mathcal {H}_{\kappa }\) ; the reproducing kernel Hilbert space (RHKS; e.g. [1]}, Section 17.5) with kernel \(\kappa (\cdot ,\cdot ; \rho )\) ; and \(J(\mu ) = \lambda \Vert \mu \Vert _{\mathcal {H}_{\kappa }}\) , where \(\Vert \cdot \Vert _{\mathcal {H}_{\kappa }}\)  is the RKHS norm. It can be shown [2]} that \(\hat{\mu }(\mathbf {x})\)  is given by
\(\hat{\mu }(\mathbf {x}) = \sum _{i=1}^n u_i \kappa (\mathbf {x}, \mathbf {x}_i; \rho ),\) 
